Spin-Orbit Coupling Effects on Ligand-Free Icosahedral Matryoshka Superatoms

With the help of density functional theory, a series of matryoshka superatoms X@Y₁₂@X₂₀ (X = Ge, Y = Zn; X = Sn, Y = Mg, Mn, Zn or Cd; X = Pb, Y = Mg, Mn, Cd or Hg) with icosahedral symmetry has been extensively studied, to focus on the influence of the spin-orbit coupling on geometries, stabilities, electronic structures and magnetic moments for these clusters. Generally speaking, the effect of spin-orbit coupling is highly correlated with composition elements of these clusters. Ge@Zn₁₂@Ge₂₀ is little affected by the spin-orbit coupling, while clusters containing Sn atom will generally undergo a moderate influence on their atomization energy, HOMO-LUMO gap and projected density of states. For clusters with Pb atoms, the effect of spin-orbit coupling could be observed distinctly in most cases. Our results demonstrate that the spin-orbit coupling can play a substantial role in superatoms containing heavy elements.